I resized all of those to the same diagonal pixel dimension and showed them to a bunch of family and friends, asking the simple question "Which of these images look equivalent to you?" When pressed to explain what I meant by equivalent, I offered the guidance "Similar in visual properties".

According to Joe's proposed definition of "equivalent images", the Leica, Fuji, and Olympus images were equivalent, and the Sony not equivalent. Indeed, I could tell that the Sony image had less DOF than the others. Yet everyone picked the Sony, Fuji, and Oly shots as equivalent, noting that the obvious difference in visual properties was how noisy the Leica image looked. The second most common observation had to do with slight differences in color rendition. No one commented on the DOF differences, including my wife who often complains about a photo being blurry when I use a narrow DOF.

To some people, a 35/1.4 on a Leica M9 doesn't produce an image equivalent to one made with a 35/1.4 on a D800. To this guy, a Canon 35/1.4 on a 5D III doesn't produce an image equivalent to one made with a Sigma 35/1.4 on a D800.

Arguing about what is equivalent is like arguing about what is compact. There is no accepted definition other than the common use as pertains to focal length equivalents. There is a proposed definition of "equivalent image" but not an accepted one.

Seems like only the "good nerds" qualify for your "acceptance". "Bad nerds" need not apply ?